I was in a monogamous marriage for 30 years, it broke up, and about 14 months later I fell for a woman who's in a polyamorous marriage.
It's a little different, in that she and her husband are very considerate when I'm around -- they are friendly and loving but don't smooch on each other. But sometimes when she and I are talking on the phone she'll say, "I have to go soon -- D is drawing us a bath." That just gives me a warm tingle -- that she's so well loved and cared for. It's GOOD!
She recently told me she had started making out with an old boyfriend but stopped because she wasn't sure how I would feel about it. But after a little consideration I thought: I may have felt hurt if she had left my arms and gone to him...but I was not available and I was not there. So maybe if it happens again I'll get a little candygram from the noosphere that will tell me L is getting happy and sexed up, and that will give me a warm tingle too.
So that's how it works for me. But I've found a lot of consideration and respect in the relationship -- I think the people I'm with have realized that while polyamory is aesthetically and ethically beautiful there are polite conventions which can make it work more smoothly.
If you and this woman are really becoming committed to a caring relationship then you might talk about what makes you comfortable and what will keep polyamory viable for you, as well as for her. If she needs you to watch things that hurt you or make you unhappy, then that's a warning sign -- exactly as it would be in a monogamous relationship.